About
A tool by a runner, for runners.
What is PaceVance?
PaceVance is a pace planning tool for road and trail runners. It helps you plan every segment of your race: not just the distance and finish time, but the real effort — accounting for climbing, descent, and terrain.
It runs entirely in your browser. No data leaves your device. No account required.
Pace algorithms
For flat or road running, pace is straightforward. For trail, elevation changes everything. PaceVance supports three established models:
Naismith's Rule
The oldest and simplest model for mountain hiking and running. Originally published by Scottish mountaineer William Naismith in 1892.
Good for: steady climbs, moderate terrain, general race planning. Use this when in doubt. We apply Langmuir's descent corrections: descents steeper than 12° cost 10 minutes per 300 m, while gentler ones (5–12°) are free speed and earn the same back.
Tobler's Hiking Function
A continuous model giving travel speed as a function of slope, from Waldo Tobler's work on terrain-adjusted travel time.
Good for: variable terrain where both ascent and descent rates matter. Gives faster speeds on slight downhills (the optimal descending angle), and accounts for the cost of braking on steep descents. Tobler's curve describes walking speed in absolute terms, so we use only its shape — the ratio against its own flat-ground speed — and apply that to your flat pace. A faster runner gets a faster adjusted pace at every gradient.
Minetti Model
Based on Minetti et al. (2002) — a lab study measuring the metabolic energy cost of running at extreme inclines. Provides the most biomechanically grounded correction.
Good for: ultra distances and very steep terrain where the other models become less accurate. Requires a known flat pace to scale from. Note this is Minetti's cost of running, Cr — the paper also fits a walking curve, Cw, whose constants differ and which would over-penalise every climb. The polynomial was fitted between −45% and +45% gradient, so we clamp to that range rather than extrapolate beyond it.
Why we show the math
Trail runners are serious planners. You know your body, your terrain, your race history. No calculator knows better than you do — it just does the arithmetic faster.
Every algorithm has assumptions baked in. Naismith was calibrated for steady hillwalking, not technical scrambling. Tobler was validated at hiking pace. Minetti is lab-measured running economy — it'll vary for your fitness level and running style.
One thing we do to all of them: a segment carries its climb and its descent separately, and we cost each part on its own before adding them up. Working from the net change instead would let a loop or an out-and-back cancel to zero and come back with flat-ground pace — which is exactly wrong for the most common shape of trail route.
Use the terrain factor (1.0–1.3) to dial in your experience from past races. 1.0 is smooth trail, 1.15 is technical singletrack, 1.3 is hands-on-knees scrambling.
How it's built
References
- Naismith, W. (1892). Excursion to Ben Lui. Scottish Mountaineering Club Journal.
- Tobler, W. (1993). Three presentations on geographical analysis and modeling. UCSB Technical Report.
- Minetti, A.E. et al. (2002). Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology, 93(3), 1039–1046.
- Langmuir, E. (1984). Mountaincraft and Leadership. Scottish Sports Council.